Abstract
Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let T-i : C -> C, i = 1, 2, ... , N, be a finite family of Lipschitz pseudocontractive mappings. It is our purpose, in this paper, to prove strong convergence of Ishikawa's method to a common fixed point of a finite family of Lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty. No compactness assumption is imposed either on T or on C. Moreover, computation of the closed convex set C-n for each n >= 1 is not required. The results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings. (C) 2011 Elsevier Ltd. All rights reserved.